Is the Rayleigh-Taylor mixing growth constant universal?
In plain words
When heavy fluid rests on light fluid under gravity, the interface overturns and a turbulent mixing zone grows with the square of time. Simulations give a growth rate about half of what experiments measure, and whether a single universal value exists is unknown.
Precise statement
For incompressible miscible Rayleigh-Taylor turbulence with Atwood number $A=(\rho_1-\rho_2)/(\rho_1+\rho_2)$ and acceleration g, the bubble penetration grows as $h_b=\alpha_b A g t^2$ at late times. Determine whether $\alpha_b$ reaches a universal limit independent of the initial interface perturbation spectrum as $h_b/\lambda_0\to \infty$ ($\lambda_0$ the dominant initial wavelength), or retains permanent memory of long-wavelength initial content, and give its value at low $A$.
What would settle it
Experiments and DNS with measured and matched initial interface spectra followed to large $h_b/\lambda_0$, showing whether $\alpha_b$ converges to a common value.
Status in the literature
The Alpha-Group comparison found simulated $\alpha_b \sim 0.025 \pm 0.003$ against experimental $0.057 \pm 0.008$ and attributed the gap partly to long-wavelength initial perturbations (Dimonte et al., Physics of Fluids 2004).